Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $a+b+c=9$ and $a b+b c+c a=-22$, then the value of $a^3+b^3+c^3-3 a b c$ is:

Options:

783

1323

1571

487

Correct Answer:

1323

Explanation:

If x + y  = n

then, $x^3 + y^3$ = n3 - 3 × n × xy

If $a+b+c=9$

$a b+b c+c a=-22$

Then the value of $a^3+b^3+c^3-3 a b c$= ?

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put c = 0

If $a+b=9$

$a b=-22$

Then the value of $a^3+b^3$= 93 - 3 × 9 × -22

Then the value of $a^3+b^3$= 1323